_igam_helper_fac Class — pytorch Architecture

Source Code

aten/src/ATen/native/Math.h lines 620–652

template <typename scalar_t>
static scalar_t _igam_helper_fac(scalar_t a, scalar_t x) {
  // compute x^a * exp(-a) / gamma(a)
  // corrected from (15) and (16) in [igam2] by replacing exp(x - a) with
  // exp(a - x).

  scalar_t ax, fac, res, num, numfac;
  static scalar_t MAXLOG = std::is_same_v<scalar_t,double> ?
    7.09782712893383996843E2 : 88.72283905206835;
  static scalar_t EXP1 = 2.718281828459045;
  static scalar_t lanczos_g = 6.024680040776729583740234375;

  if (std::fabs(a - x) > 0.4 * std::fabs(a)) {
    ax = a * std::log(x) - x - std::lgamma(a);
    if (ax < -MAXLOG) {
      return 0.0;
    }
    return std::exp(ax);
  }

  fac = a + lanczos_g - 0.5;
  res = std::sqrt(fac / EXP1) / lanczos_sum_expg_scaled(a);

  if ((a < 200) && (x < 200)) {
    res *= std::exp(a - x) * std::pow(x / fac, a);
  }
  else {
    num = x - a - lanczos_g + 0.5;
    numfac = num / fac;
    res *= std::exp(a * (std::log1p(numfac) - numfac) + x * (0.5 - lanczos_g) / fac);
  }
  return res;
}